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A losing estimate for the ideal MHD equations with application to blow-up criterion

Abstract : In this paper we study the blow-up criterion of smooth solution to the ideal MHD equations in R-n. By means of the Fourier frequency localization and Bony paraproduct decomposition, we show a losing estimate for the ideal MHD equations and apply it to establish an improved blow-up criterion of smooth solutions. As a special case, we recover a previous result of Planchon for the incompressible Euler equations.
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Submitted on : Wednesday, May 2, 2012 - 11:40:37 PM
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Marco Cannone, Qionglei Chen, Changxing Miao. A losing estimate for the ideal MHD equations with application to blow-up criterion. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2006, 38 (6), pp.1847--1859. ⟨10.1137/060652002⟩. ⟨hal-00693787⟩

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